Fast algorithms for determining the linear complexities of sequences over GF(pm) with the period 3n |
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Authors: | Chen Hao |
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Institution: | (1) Department of Computing and Information Technology, Fudan University, Shanghai, 200433, China |
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Abstract: | In this paper, for the the primes p such that 3 is a divisor of p − 1, we prove a result which reduces the computation of the linear complexity of a sequence over GF(p
m) (any positive integer m) with the period 3n (n and p
m − 1 are coprime) to the computation of the linear complexities of three sequences with the period n. Combined with some known algorithms such as generalized Games-Chan algorithm, Berlekamp-Massey algorithm and Xiao-Wei-Lam-Imamura
algorithm, we can determine the linear complexity of any sequence over GF(p
m) with the period 3n (n and p
m
− 1 are coprime) more efficiently. |
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Keywords: | number theory of the finite field cryptography stream cipher fast algorithm |
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